Entanglement Entropy of Black Holes and Anti–de Sitter Space/Conformal-Field-Theory Correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti–de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti–de Sitter space. The generalized proposal is verified in boundary dimensions $d=2$ and $d=4$ for both the uv-divergent and uv-finite terms. In dimension $d=4$ an expansion of entanglement entropy in terms of size $L$ of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as $L^2\ln L$ and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.